2008 AMC 12B Problems/Problem 18
Problem
A pyramid has a square base and vertex . The area of square is , and the areas of and are and , respectively. What is the volume of the pyramid?
Solution
Let be the height of the pyramid and be the distance from to . The side length of the base is . The heights of and are and , respectively. Consider a side view of the pyramid from . We have a systems of equations through the Pythagorean Theorem:
Setting them equal to each other and simplifying gives .
Therefore, , and the volume of the pyramid is .
See also
2008 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 17 |
Followed by Problem 19 |
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All AMC 12 Problems and Solutions |
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